Finite Group Databasebeta

← #13172324

Subgroups — #13172324

Order 1728.

1706 conjugacy classes of subgroups.

The subgroup lattice has 948 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#626C211yesmaximal, characteristic, complemented
2C2×C3×#3804C211yesmaximal, characteristic, complemented
3#11723727C211yesmaximal, characteristic, complemented
4#11723634C211yesmaximal, characteristic, complemented
5#11723629C211yesmaximal, characteristic, complemented
6#11723594C211yesmaximal, characteristic, complemented
7C3×#63976C211yesmaximal, characteristic, complemented
8#11723029C212yesmaximal, complemented
9#11723001C212yesmaximal, complemented
10#11722957C212yesmaximal, complemented
11#11722956C212yesmaximal, complemented
12#10595513—31nomaximal
13#10595238—31nomaximal
14#10595040—31nomaximal
15C23×C3×C3⋊D3C2211yescharacteristic
16C23×C32×D3C2211yescharacteristic
17C2×C3×#638C2211yescharacteristic
18C2×C32×#67C2211yescharacteristic
19C22×C32×Dic3C2211yescharacteristic
20C2×#6295C2212yescomplemented
21C2×#6290C2212yescomplemented
22C2×#6290C2212yescomplemented
23C2×C3×#627C2211yescharacteristic, complemented
24C2×C3×#626—24no—
25C2×C3×#626C2212yes—
26C2×C3×#626C2212yes—
27C2×C3×#626C2211yescharacteristic, complemented
28C2×C3×#625C2212yescomplemented
29C2×C3×#624C2211yescharacteristic, complemented
30C3×#3804—24no—
31C2×C3×D3×Dic3C2211yescharacteristic, complemented
32#88864C2211yescharacteristic
33C3×#3757C2211yescharacteristic
34#88814C2212yescomplemented
35Dic3⋊(C3⋊Dic3)C2212yescomplemented
36#88803C2212yescomplemented
37(C2×D3)⋊(C3⋊Dic3)C2212yescomplemented
38Dic3×C3⋊Dic3C2212yescomplemented
39C3×(C2×D3)⋊Dic3C2212yescomplemented
40C22×C3×#67—31no—
41C2×C3×#237—31no—
42C2×C3×#235—31no—
43C22×C3×D12—31no—
44C22×#626D311yescharacteristic, complemented
45C2×#3804D311yescharacteristic, complemented
46#64162—31no—
47#64146—31no—
48#64135—31no—
49C3×#953—31no—
50C3×#937—31no—
51#63981—31no—
52#63979—32no—
53#63979—32no—
54#63978—32no—
55#63977—31no—
56#63976—31no—
57#63976—31no—
58#63976—31no—
59#63976—31no—
60#63976—31no—
61#63976—61no—
62#63976—61no—
63#63976D311yescharacteristic, complemented
64#63970—32no—
65#63959—32no—
66#63958—32no—
67#63955—31no—
68#63955—31no—
69#63955—61no—
70#63914—32no—
71#63908—32no—
72#63908—32no—
73#63907—32no—
74#63906—32no—
75#63863—32no—
76C23×C33C2311yescharacteristic
77C22×C3×C3⋊D3—22no—
78C22×C3×C3⋊D3—42no—
79C22×C3×C3⋊D3C2312yes—
80C22×C3×C3⋊D3C2311yescharacteristic
81C22×C32×D3—22no—
82C22×C32×D3—42no—
83C22×C32×D3C2312yes—
84C22×C32×D3C2311yescharacteristic
85C2×C3⋊(C3⋊Dic3)C2312yes—
86C3×#638—22no—
87C2×C3×C3⋊Dic3C2312yes—
88C2×C3×C3⋊Dic3C2311yescharacteristic
89C32×#67—22no—
90C2×C32×Dic3D414yescomplemented
91C2×C32×Dic3C2311yescharacteristic
92C2×C32×Dic3C2311yescharacteristic
93C2×C32×Dic3C2311yescharacteristic
94#6295—42no—
95#6290—42no—
96#6290—42no—
97C3×#627—22no—
98C3×#626—22no—
99C3×#626—24no—
100C3×#626—24no—
101C3×#625—42no—
102C3×#624—22no—
103C3×D3×Dic3—22no—
104#5830—91no—
105#5805—91no—
106#5592—91no—
107C24×C32—31no—
108C23×C3⋊D3C2×D311yescharacteristic
109C23×C3×D3—21no—
110C23×C3×D3—31no—
111C23×C3×D3—31no—
112C23×C3×D3—61no—
113C23×C3×D3C2×D311yescharacteristic
114C23×C3×D3C2×D311yescharacteristic
115C2×C32×D4—31no—
116C22×C32×C4—31no—
117C2×#638—32no—
118C2×#638—32no—
119C2×#638C2×D311yescharacteristic
120C2×C3×#67—21no—
121C2×C3×#67—31no—
122C2×C3×#67—31no—
123C2×C3×#67—32no—
124C2×C3×#67—32no—
125C2×C3×#67—31no—
126C2×C3×#67—32no—
127C2×C3×#67—32no—
128C2×C3×#67—61no—
129C2×C3×#67—64no—
130C2×C3×#67C2×D311yescharacteristic
131C2×C3×#67C2×D311yescharacteristic
132C22×C3×Dic3—21no—
133C22×C3×Dic3—31no—
134C22×C3×Dic3C2×D311yescharacteristic
135C22×C3×Dic3C2×D311yescharacteristic
136C3×#237—64no—
137C3×#235—64no—
138C2×C3×D12—32no—
139C2×C3×D12—32no—
140C2×C3×D12—31no—
141C2×C3×D12—64no—
142C2×C3×C4×D3—31no—
143C2×C3×C4×D3—31no—
144C2×C3×C4×D3—31no—
145C2×C3×Dic6—31no—
146C2×C3×Dic6—31no—
147C2×#627C2×D311yescharacteristic, complemented
148C2×#626—24no—
149C2×#626—32no—
150C2×#626—32no—
151C2×#626C2×D312yes—
152C2×#626C2×D312yes—
153C2×#626C2×D311yescharacteristic, complemented
154C2×#625—32no—
155C2×#625—32no—
156C2×#625—32no—
157C2×#625—32no—
158C2×#625—32no—
159C2×#625—62no—
160C2×#625—62no—
161C2×#625C2×D312yescomplemented
162C2×#624C2×D311yescharacteristic, complemented
163#3804—24no—
164C2×D3×Dic3C2×D311yescharacteristic, complemented
165#3757—31no—
166#3757—31no—
167#3757—31no—
168#3757—32no—
169#3757—61no—
170#3757—61no—
171#3757—61no—
172#3757—121no—
173#3757C2×D311yescharacteristic
174#3752—32no—
175C4⋊(C3⋊Dic3)—32no—
176C4×C3⋊Dic3—32no—
177C3×#217—31no—
178C3×#217—31no—
179C3×#217—32no—
180C3×#217—61no—
181C3×(C2×D3)⋊C4—32no—
182Dic3⋊Dic3—32no—
183Dic3⋊Dic3—32no—
184Dic3⋊Dic3—62no—
185#3722—32no—
186(C2×D3)⋊Dic3—32no—
187(C2×D3)⋊Dic3—32no—
188(C2×D3)⋊Dic3—32no—
189(C2×D3)⋊Dic3—32no—
190(C2×D3)⋊Dic3—32no—
191(C2×D3)⋊Dic3—32no—
192(C2×D3)⋊Dic3—62no—
193(C2×D3)⋊Dic3—62no—
194(C2×D3)⋊Dic3C2×D312yescomplemented
195Dic32—32no—
196Dic32—32no—
197Dic32—62no—
198C22×C33—22no—
199C22×C33C2×D412yes—
200C22×C33C2411yescharacteristic
201C2×C3×C3⋊D3—21no—
202C2×C3×C3⋊D3—22no—
203C2×C3×C3⋊D3—22no—
204C2×C3×C3⋊D3—22no—
205C2×C3×C3⋊D3—22no—
206C2×C3×C3⋊D3—44no—
207C2×C32×D3—21no—
208C2×C32×D3—22no—
209C2×C32×D3—22no—
210C2×C32×D3—22no—
211C2×C32×D3—22no—
212C2×C32×D3—44no—
213C3⋊(C3⋊Dic3)—22no—
214C3×C3⋊Dic3—21no—
215C3×C3⋊Dic3—22no—
216C32×Dic3—21no—
217C32×Dic3C2×D412yes—
218C32×Dic3C2×D412yes—
219C2×C3×#41—91no—
220C22×C3×D4—91no—
221C22×#67—31no—
222C2×#237—31no—
223C2×#235—31no—
224C22×D12—31no—
225C3×#120—91no—
226#953—31no—
227#953—91no—
228#953—91no—
229#953—91no—
230#953—91no—
231#953—181no—
232#947—92no—
233#940—92no—
234#940—92no—
235#940—92no—
236#939—92no—
237#938—92no—
238#938—92no—
239#937—31no—
240#937—91no—
241#937—91no—
242#937—91no—
243#937—91no—
244#937—181no—
245#936—92no—
246#930—92no—
247#930—92no—
248#926—91no—
249#926—91no—
250#926—181no—
251#885—92no—
252#884—92no—
253#882—91no—
254#877—91no—
255C23×C32—21no—
256C23×C32—21no—
257C23×C32—21no—
258C23×C32—32no—
259C23×C32—31no—
260C23×C32—41no—
261C23×C32—62no—
262C23×C32—122no—
263C23×C32C22×D311yescharacteristic
264C23×C32C22×D311yescharacteristic
265C23×C32C22×D311yescharacteristic
266C22×C3⋊D3—22no—
267C22×C3⋊D3—42no—
268C22×C3⋊D3C22×D312yes—
269C22×C3⋊D3C22×D311yescharacteristic
270C22×C3×D3—22no—
271C22×C3×D3—22no—
272C22×C3×D3—22no—
273C22×C3×D3—21no—
274C22×C3×D3—32no—
275C22×C3×D3—32no—
276C22×C3×D3—31no—
277C22×C3×D3—31no—
278C22×C3×D3—42no—
279C22×C3×D3—42no—
280C22×C3×D3—42no—
281C22×C3×D3—44no—
282C22×C3×D3—62no—
283C22×C3×D3—61no—
284C22×C3×D3—62no—
285C22×C3×D3—62no—
286C22×C3×D3—122no—
287C22×C3×D3—122no—
288C22×C3×D3—122no—
289C22×C3×D3—124no—
290C22×C3×D3C22×D312yes—
291C22×C3×D3C22×D312yes—
292C22×C3×D3C22×D311yescharacteristic
293C22×C3×D3C22×D311yescharacteristic
294C32×D4—62no—
295C2×C32×C4—34no—
296C2×C32×C4—31no—
297C2×C32×C4—31no—
298C2×C32×C4—31no—
299#638—22no—
300#638—122no—
301#638—122no—
302C2×C3⋊Dic3—32no—
303C2×C3⋊Dic3—32no—
304C2×C3⋊Dic3—32no—
305C2×C3⋊Dic3—62no—
306C2×C3⋊Dic3—62no—
307C2×C3⋊Dic3—62no—
308C2×C3⋊Dic3—122no—
309C2×C3⋊Dic3C22×D311yescharacteristic
310C2×C3⋊Dic3C22×D312yes—
311C3×#67—22no—
312C3×#67—22no—
313C3×#67—42no—
314C3×#67—62no—
315C3×#67—62no—
316C3×#67—62no—
317C3×#67—64no—
318C3×#67—64no—
319C3×#67—122no—
320C3×#67—122no—
321C3×#67—122no—
322C2×C3×Dic3—24no—
323C2×C3×Dic3—21no—
324C2×C3×Dic3—21no—
325C2×C3×Dic3—21no—
326C2×C3×Dic3—32no—
327C2×C3×Dic3—32no—
328C2×C3×Dic3—31no—
329C2×C3×Dic3—31no—
330C2×C3×Dic3—62no—
331C2×C3×Dic3—61no—
332C2×C3×Dic3—62no—
333C2×C3×Dic3#6714yescomplemented
334C2×C3×Dic3#6714yescomplemented
335C2×C3×Dic3C22×D311yescharacteristic
336C2×C3×Dic3C22×D311yescharacteristic
337C2×C3×Dic3C22×D311yescharacteristic
338C2×C3×Dic3C22×D311yescharacteristic
339C2×C3×Dic3C22×D311yescharacteristic
340C2×C3×Dic3C22×D311yescharacteristic
341C3×D12—64no—
342C3×D12—64no—
343C3×D12—62no—
344C3×C4×D3—62no—
345C3×C4×D3—62no—
346C3×C4×D3—62no—
347C3×Dic6—62no—
348C3×Dic6—62no—
349#627—22no—
350#626—22no—
351#626—24no—
352#626—24no—
353#626—122no—
354#626—122no—
355#625—42no—
356#625—122no—
357#625—122no—
358#625—122no—
359#625—122no—
360#625—122no—
361#625—124no—
362#625—124no—
363#624—22no—
364D3×Dic3—22no—
365#535—271noSylow
366C2×C33—22no—
367C2×C33C22×D411yescharacteristic
368C2×C33H(5,𝔽2)12yes—
369C3×C3⋊D3—42no—
370C3×C3⋊D3—41no—
371C32×D3—42no—
372C32×D3—41no—
373C24×C3—31no—
374C24×C3—31no—
375C24×C3—61no—
376C24×C3—91no—
377C23×D3—31no—
378C23×D3—31no—
379C23×D3—61no—
380C23×D3D3211yescharacteristic
381C3×#41—184no—
382C2×C3×Q8—91no—
383C2×C3×D4—31no—
384C2×C3×D4—31no—
385C2×C3×D4—61no—
386C2×C3×D4—92no—
387C2×C3×D4—92no—
388C2×C3×D4—91no—
389C2×C3×D4—91no—
390C2×C3×D4—92no—
391C2×C3×D4—184no—
392C22×C3×C4—31no—
393C22×C3×C4—31no—
394C22×C3×C4—61no—
395C22×C3×C4—91no—
396C22×C3×C4—91no—
397C2×#67—31no—
398C2×#67—31no—
399C2×#67—32no—
400C2×#67—32no—
401C2×#67—32no—
402C2×#67—32no—
403C2×#67—31no—
404C2×#67—61no—
405C2×#67—64no—
406C2×#67—92no—
407C2×#67—92no—
408C2×#67—92no—
409C2×#67—92no—
410C2×#67—92no—
411C2×#67—92no—
412C2×#67—92no—
413C2×#67—92no—
414C2×#67—182no—
415C2×#67—182no—
416C2×#67D3211yescharacteristic
417C22×Dic3—31no—
418C22×Dic3D3211yescharacteristic
419#237—64no—
420#235—64no—
421C2×D12—32no—
422C2×D12—31no—
423C2×D12—32no—
424C2×D12—64no—
425C2×D12—92no—
426C2×C4×D3—31no—
427C2×C4×D3—31no—
428C2×C4×D3—31no—
429C2×Dic6—31no—
430C2×Dic6—31no—
431C3×C22⋊C4—92no—
432C3×C22⋊C4—91no—
433#217—31no—
434#217—31no—
435#217—32no—
436#217—61no—
437#217—92no—
438#217—92no—
439#217—92no—
440#217—91no—
441#217—91no—
442#217—91no—
443#217—92no—
444#217—182no—
445#217—181no—
446#217—181no—
447#217—181no—
448#217—361no—
449(C2×D3)⋊C4—32no—
450(C2×D3)⋊C4—92no—
451(C2×D3)⋊C4—92no—
452(C2×D3)⋊C4—92no—
453(C2×D3)⋊C4—92no—
454(C2×D3)⋊C4—92no—
455(C2×D3)⋊C4—182no—
456C4⋊Dic3—92no—
457C4⋊Dic3—92no—
458C4⋊Dic3—182no—
459Dic3⋊C4—92no—
460C4×Dic3—92no—
461C4×Dic3—92no—
462C4×Dic3—92no—
463C4×Dic3—182no—
464C22×C32—22no—
465C22×C32—22no—
466C22×C32—22no—
467C22×C32—21no—
468C22×C32—21no—
469C22×C32—21no—
470C22×C32—22no—
471C22×C32—22no—
472C22×C32—22no—
473C22×C32—41no—
474C22×C32—42no—
475C22×C32—42no—
476C22×C32—42no—
477C22×C32—42no—
478C22×C32—62no—
479C22×C32—62no—
480C22×C32—62no—
481C22×C32—61no—
482C22×C32—62no—
483C22×C32—82no—
484C22×C32—124no—
485C22×C32D3×D412yes—
486C22×C32C2×#6712yes—
487C22×C32C2×#6712yes—
488C22×C32C23×D311yescharacteristic
489C22×C32C23×D311yescharacteristic
490C22×C32C23×D311yescharacteristic
491C2×C3⋊D3—22no—
492C2×C3⋊D3—22no—
493C2×C3⋊D3—22no—
494C2×C3⋊D3—21no—
495C2×C3⋊D3—22no—
496C2×C3⋊D3—44no—
497C2×C3×D3—24no—
498C2×C3×D3—21no—
499C2×C3×D3—22no—
500C2×C3×D3—22no—
501C2×C3×D3—22no—
502C2×C3×D3—22no—
503C2×C3×D3—22no—
504C2×C3×D3—22no—
505C2×C3×D3—22no—
506C2×C3×D3—21no—
507C2×C3×D3—22no—
508C2×C3×D3—42no—
509C2×C3×D3—42no—
510C2×C3×D3—42no—
511C2×C3×D3—41no—
512C2×C3×D3—44no—
513C2×C3×D3—44no—
514C2×C3×D3—48no—
515C2×C3×D3—64no—
516C2×C3×D3—61no—
517C2×C3×D3—62no—
518C2×C3×D3—62no—
519C2×C3×D3—62no—
520C2×C3×D3—62no—
521C2×C3×D3—62no—
522C2×C3×D3—62no—
523C2×C3×D3—62no—
524C2×C3×D3—61no—
525C2×C3×D3—62no—
526C2×C3×D3—122no—
527C2×C3×D3—122no—
528C2×C3×D3—122no—
529C2×C3×D3—121no—
530C2×C3×D3—124no—
531C2×C3×D3—124no—
532C2×C3×D3—128no—
533C32×C4—32no—
534C32×C4—32no—
535C32×C4—61no—
536C3⋊Dic3—22no—
537C3⋊Dic3—21no—
538C3⋊Dic3—62no—
539C3⋊Dic3—62no—
540C3⋊Dic3—62no—
541C3⋊Dic3—122no—
542C3⋊Dic3—122no—
543C3⋊Dic3—122no—
544C3⋊Dic3—242no—
545C3×Dic3—21no—
546C3×Dic3—21no—
547C3×Dic3—22no—
548C3×Dic3—22no—
549C3×Dic3—41no—
550C3×Dic3—61no—
551C3×Dic3—62no—
552C3×Dic3—62no—
553C3×Dic3—61no—
554C3×Dic3—122no—
555C3×Dic3—121no—
556C3×Dic3C2×#6712yes—
557C3×Dic3C2×#6712yes—
558C3×Dic3C2×#6712yes—
559C3×Dic3C2×#6712yes—
560C2×#41—91no—
561C22×D4—91no—
562#127—272no—
563#124—272no—
564#121—272no—
565#121—272no—
566#120—91no—
567#120—271no—
568#120—271no—
569#120—271no—
570#117—271no—
571C33#53511yescharacteristic, complemented, Sylow
572C23×C3—21no—
573C23×C3—21no—
574C23×C3—21no—
575C23×C3—32no—
576C23×C3—32no—
577C23×C3—31no—
578C23×C3—31no—
579C23×C3—41no—
580C23×C3—62no—
581C23×C3—61no—
582C23×C3—62no—
583C23×C3—62no—
584C23×C3—92no—
585C23×C3—91no—
586C23×C3—122no—
587C23×C3—122no—
588C23×C3—122no—
589C23×C3—124no—
590C23×C3—182no—
591C23×C3—362no—
592C23×C3C2×D3211yescharacteristic
593C23×C3C2×D3211yescharacteristic
594C23×C3C2×D3211yescharacteristic
595C22×D3—22no—
596C22×D3—32no—
597C22×D3—32no—
598C22×D3—31no—
599C22×D3—31no—
600C22×D3—42no—
601C22×D3—62no—
602C22×D3—61no—
603C22×D3—62no—
604C22×D3—62no—
605C22×D3—122no—
606C22×D3—122no—
607C22×D3—122no—
608C22×D3—124no—
609C22×D3C2×D3212yes—
610C22×D3C2×D3211yescharacteristic
611C3×Q8—182no—
612C3×D4—62no—
613C3×D4—62no—
614C3×D4—122no—
615C3×D4—184no—
616C3×D4—184no—
617C3×D4—182no—
618C3×D4—182no—
619C3×D4—362no—
620C2×C3×C4—31no—
621C2×C3×C4—31no—
622C2×C3×C4—31no—
623C2×C3×C4—31no—
624C2×C3×C4—34no—
625C2×C3×C4—34no—
626C2×C3×C4—31no—
627C2×C3×C4—31no—
628C2×C3×C4—61no—
629C2×C3×C4—61no—
630C2×C3×C4—64no—
631C2×C3×C4—61no—
632C2×C3×C4—92no—
633C2×C3×C4—91no—
634C2×C3×C4—182no—
635C2×C3×C4—182no—
636#67—22no—
637#67—62no—
638#67—62no—
639#67—62no—
640#67—64no—
641#67—64no—
642#67—122no—
643#67—122no—
644#67—122no—
645#67—362no—
646#67—362no—
647#67—362no—
648#67—362no—
649#67—362no—
650#67—362no—
651#67—362no—
652#67—362no—
653#67—364no—
654#67—364no—
655C2×Dic3—32no—
656C2×Dic3—32no—
657C2×Dic3—31no—
658C2×Dic3—31no—
659C2×Dic3—62no—
660C2×Dic3—61no—
661C2×Dic3—62no—
662C2×Dic3—92no—
663C2×Dic3—92no—
664C2×Dic3—92no—
665C2×Dic3—182no—
666C2×Dic3—182no—
667C2×Dic3—182no—
668C2×Dic3—362no—
669C2×Dic3#62514yescomplemented
670C2×Dic3C2×D3211yescharacteristic
671C2×Dic3C2×D3211yescharacteristic
672C2×Dic3C2×D3211yescharacteristic
673D12—64no—
674D12—64no—
675D12—62no—
676D12—362no—
677C4×D3—62no—
678C4×D3—62no—
679C4×D3—62no—
680Dic6—62no—
681Dic6—62no—
682C2×C32—22no—
683C2×C32—22no—
684C2×C32—22no—
685C2×C32—22no—
686C2×C32—22no—
687C2×C32—21no—
688C2×C32—21no—
689C2×C32—21no—
690C2×C32—22no—
691C2×C32—41no—
692C2×C32—42no—
693C2×C32—42no—
694C2×C32—42no—
695C2×C32—42no—
696C2×C32—82no—
697C2×C32—122no—
698C2×C32—121no—
699C2×C32C2×D3×D411yescharacteristic
700C2×C32#100412yes—
701C2×C32#100412yes—
702C2×C32#100912yes—
703C2×C32C22×#6711yescharacteristic
704C2×C32C22×#6711yescharacteristic
705C3⋊D3—42no—
706C3⋊D3—41no—
707C3×D3—44no—
708C3×D3—42no—
709C3×D3—41no—
710C3×D3—41no—
711C3×D3—42no—
712C3×D3—81no—
713C3×D3—124no—
714C3×D3—121no—
715C3×D3—122no—
716C3×D3—121no—
717C3×D3—122no—
718C3×D3—241no—
719C24—31no—
720C24—91no—
721#41—184no—
722C2×Q8—91no—
723C2×D4—31no—
724C2×D4—92no—
725C2×D4—92no—
726C2×D4—91no—
727C2×D4—91no—
728C2×D4—92no—
729C2×D4—184no—
730C2×D4—272no—
731C2×D4—272no—
732C2×D4—272no—
733C22×C4—31no—
734C22×C4—91no—
735C22×C4—91no—
736C4⋊C4—272no—
737C22⋊C4—92no—
738C22⋊C4—91no—
739C22⋊C4—272no—
740C22⋊C4—272no—
741C22⋊C4—272no—
742C22⋊C4—271no—
743C42—272no—
744C22×C3—22no—
745C22×C3—22no—
746C22×C3—22no—
747C22×C3—21no—
748C22×C3—21no—
749C22×C3—21no—
750C22×C3—22no—
751C22×C3—22no—
752C22×C3—22no—
753C22×C3—42no—
754C22×C3—42no—
755C22×C3—42no—
756C22×C3—41no—
757C22×C3—42no—
758C22×C3—64no—
759C22×C3—62no—
760C22×C3—62no—
761C22×C3—62no—
762C22×C3—62no—
763C22×C3—62no—
764C22×C3—61no—
765C22×C3—62no—
766C22×C3—61no—
767C22×C3—62no—
768C22×C3—62no—
769C22×C3—82no—
770C22×C3—122no—
771C22×C3—122no—
772C22×C3—122no—
773C22×C3—121no—
774C22×C3—124no—
775C22×C3—124no—
776C22×C3—128no—
777C22×C3—182no—
778C22×C3—182no—
779C22×C3—181no—
780C22×C3—182no—
781C22×C3—182no—
782C22×C3—364no—
783C22×C3C2×#62512yes—
784C22×C3D3×#6712yes—
785C22×C3D3×#6712yes—
786C22×C3C22×D3211yescharacteristic
787C22×C3C22×D3211yescharacteristic
788C22×C3C22×D3211yescharacteristic
789C2×D3—22no—
790C2×D3—21no—
791C2×D3—22no—
792C2×D3—22no—
793C2×D3—22no—
794C2×D3—44no—
795C2×D3—64no—
796C2×D3—62no—
797C2×D3—62no—
798C2×D3—62no—
799C2×D3—62no—
800C2×D3—61no—
801C2×D3—62no—
802C2×D3—61no—
803C2×D3—62no—
804C2×D3—62no—
805C2×D3—62no—
806C2×D3—122no—
807C2×D3—122no—
808C2×D3—121no—
809C2×D3—122no—
810C2×D3—124no—
811C2×D3—124no—
812C2×D3—128no—
813C3×C4—32no—
814C3×C4—32no—
815C3×C4—32no—
816C3×C4—32no—
817C3×C4—62no—
818C3×C4—62no—
819C3×C4—61no—
820C3×C4—61no—
821C3×C4—121no—
822C3×C4—182no—
823C3×C4—181no—
824Dic3—21no—
825Dic3—62no—
826Dic3—61no—
827Dic3—61no—
828Dic3—62no—
829Dic3—121no—
830Dic3—122no—
831Dic3—182no—
832Dic3—182no—
833Dic3—182no—
834Dic3—362no—
835Dic3—362no—
836Dic3—362no—
837Dic3—722no—
838Dic3C2×#62512yes—
839Dic3C2×#62512yes—
840C32—21no—
841C32—21no—
842C32—21no—
843C32—41no—
844C32#559211yescharacteristic, complemented
845C32#580511yescharacteristic, complemented
846C32#583011yescharacteristic, complemented
847C23—32no—
848C23—31no—
849C23—62no—
850C23—92no—
851C23—91no—
852C23—122no—
853C23—182no—
854C23—362no—
855C23D3311yescharacteristic
856Q8—182no—
857D4—62no—
858D4—184no—
859D4—184no—
860D4—182no—
861D4—182no—
862D4—362no—
863D4—1082no—
864D4—1082no—
865D4—1082no—
866C2×C4—31no—
867C2×C4—31no—
868C2×C4—34no—
869C2×C4—31no—
870C2×C4—92no—
871C2×C4—91no—
872C2×C4—182no—
873C2×C4—182no—
874C2×C4—272no—
875C2×C3—22no—
876C2×C3—22no—
877C2×C3—22no—
878C2×C3—21no—
879C2×C3—21no—
880C2×C3—21no—
881C2×C3—22no—
882C2×C3—22no—
883C2×C3—22no—
884C2×C3—42no—
885C2×C3—42no—
886C2×C3—42no—
887C2×C3—41no—
888C2×C3—42no—
889C2×C3—82no—
890C2×C3—124no—
891C2×C3—122no—
892C2×C3—121no—
893C2×C3—122no—
894C2×C3—121no—
895C2×C3—241no—
896C2×C3—362no—
897C2×C3—361no—
898C2×C3#6430712yes—
899C2×C3#6431412yes—
900C2×C3C22×#62511yescharacteristic
901C2×C3C2×D3×#6711yescharacteristic
902C2×C3C2×D3×#6711yescharacteristic
903C2×C3#6433012yes—
904D3—41no—
905D3—42no—
906D3—124no—
907D3—121no—
908D3—122no—
909D3—122no—
910D3—121no—
911D3—241no—
912C22—22no—
913C22—61no—
914C22—62no—
915C22—62no—
916C22—62no—
917C22—62no—
918C22—124no—
919C22—181no—
920C22—182no—
921C22—182no—
922C22—182no—
923C22—182no—
924C22—364no—
925C22D3×#62512yes—
926C22C2×D3311yescharacteristic
927C4—32no—
928C4—32no—
929C4—61no—
930C4—181no—
931C4—182no—
932C4—542no—
933C3—21no—
934C3—21no—
935C3—21no—
936C3—41no—
937C3#1059504011yescharacteristic, complemented
938C3#1059523811yescharacteristic, complemented
939C3#1059551311yescharacteristic, complemented
940C2—22no—
941C2—122no—
942C2—121no—
943C2—362no—
944C2—361no—
945C2C2×D3×#62511yescharacteristic
946C2#1172441812yes—
subgroupG/H
center, FrattiniC22C2×D33
commutator, socle, cosocleC22×C33C24
FittingC23×C33C23
hypercenterC23D33
hypocenterC33#535
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C23

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C22×C3×#626C2semidirect
2. C2×C3×#3804C2semidirect
3. #11723727C2semidirect
4. #11723634C2semidirect
5. #11723629C2semidirect
6. #11723594C2semidirect
7. C3×#63976C2semidirect
8. #11723029C2semidirect
9. #11723001C2semidirect
10. #11722957C2semidirect
11. #11722956C2semidirect
20. C2×#6295C22semidirect
21. C2×#6290C22semidirect
22. C2×#6290C22semidirect
23. C2×C3×#627C22semidirect
27. C2×C3×#626C22semidirect
28. C2×C3×#625C22semidirect
29. C2×C3×#624C22semidirect
31. C2×C3×D3×Dic3C22semidirect
34. #88814C22semidirect
35. Dic3⋊(C3⋊Dic3)C22semidirect
36. #88803C22semidirect
37. (C2×D3)⋊(C3⋊Dic3)C22semidirect
38. Dic3×C3⋊Dic3C22semidirect
39. C3×(C2×D3)⋊Dic3C22semidirect
44. C22×#626D3semidirect
45. C2×#3804D3semidirect
63. #63976D3semidirect
90. C2×C32×Dic3D4semidirect
147. C2×#627C2×D3semidirect
153. C2×#626C2×D3semidirect
161. C2×#625C2×D3semidirect
162. C2×#624C2×D3semidirect
164. C2×D3×Dic3C2×D3semidirect
194. (C2×D3)⋊Dic3C2×D3semidirect
333. C2×C3×Dic3#67semidirect
334. C2×C3×Dic3#67semidirect
571. C33#535semidirect
669. C2×Dic3#625semidirect
844. C32#5592semidirect
845. C32#5805semidirect
846. C32#5830semidirect
937. C3#10595040semidirect
938. C3#10595238semidirect
939. C3#10595513semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C22×C3×#6262
C2×C3×#38042
#117237272
#117236342
#117236292
#117235942
C3×#639762
#117230292
#117230012
#117229572
#117229562
#105955133
#105952383
#105950403